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Volume 28, Issue 2
Extended Synchronous Variational Integrators for Wave Propagations on Non-Uniform Meshes

Pei Liu, Jerry Zhijian Yang & Cheng Yuan

DOI: 10.4208/cicp.OA-2019-0167

Commun. Comput. Phys., 28 (2020), pp. 691-722.

Published online: 2020-06

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  • Abstract

This paper is concerned with the classical problem of wave propagation in discrete models of nonuniform resolution. We extend the traditional asynchronous variational integrators (AVIs) method to higher order and couple different spatial elements to adapt to nonuniform meshes. We show that the extension of AVIs method is stable, convergent and may reduce the spurious inter-grid reflection across meshes with different sizes. Numerical experiments are provided to verify the stability and convergence of the extended AVIs. The total energy is numerically conserved in our experiments.

  • Keywords

Asynchronous variational integrators, nonuniform mesh, local time stepping, spurious reflections.

  • AMS Subject Headings

35L05, 35A15, 65M22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-691, author = {Liu , PeiZhijian Yang , Jerry and Yuan , Cheng}, title = {Extended Synchronous Variational Integrators for Wave Propagations on Non-Uniform Meshes}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {2}, pages = {691--722}, abstract = {

This paper is concerned with the classical problem of wave propagation in discrete models of nonuniform resolution. We extend the traditional asynchronous variational integrators (AVIs) method to higher order and couple different spatial elements to adapt to nonuniform meshes. We show that the extension of AVIs method is stable, convergent and may reduce the spurious inter-grid reflection across meshes with different sizes. Numerical experiments are provided to verify the stability and convergence of the extended AVIs. The total energy is numerically conserved in our experiments.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0167}, url = {http://global-sci.org/intro/article_detail/cicp/16950.html} }
TY - JOUR T1 - Extended Synchronous Variational Integrators for Wave Propagations on Non-Uniform Meshes AU - Liu , Pei AU - Zhijian Yang , Jerry AU - Yuan , Cheng JO - Communications in Computational Physics VL - 2 SP - 691 EP - 722 PY - 2020 DA - 2020/06 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2019-0167 UR - https://global-sci.org/intro/article_detail/cicp/16950.html KW - Asynchronous variational integrators, nonuniform mesh, local time stepping, spurious reflections. AB -

This paper is concerned with the classical problem of wave propagation in discrete models of nonuniform resolution. We extend the traditional asynchronous variational integrators (AVIs) method to higher order and couple different spatial elements to adapt to nonuniform meshes. We show that the extension of AVIs method is stable, convergent and may reduce the spurious inter-grid reflection across meshes with different sizes. Numerical experiments are provided to verify the stability and convergence of the extended AVIs. The total energy is numerically conserved in our experiments.

Liu , PeiZhijian Yang , Jerry and Yuan , Cheng. (2020). Extended Synchronous Variational Integrators for Wave Propagations on Non-Uniform Meshes. Communications in Computational Physics. 28 (2). 691-722. doi:10.4208/cicp.OA-2019-0167
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